## Mathematical Physics research themes

Mathematical Physics research outputs

There is a deep and astonishingly rich interplay between mathematics and physics. Many of the most important fundamental laws of nature were discovered using purely mathematical ideas; on the other hand, several of the major themes of research in mathematics were stimulated by questions and concepts coming from physics.

We are interested in a range of areas of research connecting mathematics and physics. One involves the statistical behaviour of complex systems. In the case of classical systems, we seek to understand how simple collective behaviour emerges from complex interactions; in complex quantum systems, we study connections with the theory of random matrices. Random matrix theory is related to an enormously wide range of areas of mathematics and science, from biology to quantum gravity. We are particularly interested in connections with number theory, including the behaviour of the Riemann zeta function. Bristol has a long and distinguished history of contributions to quantum chaos, random matrix theory and interactions with number theory; several foundational ideas were developed here.

Quantum Mechanics is an extraordinarily interesting and important physical theory. Many of the most significant technological developments of the past century have at their heart novel quantum phenomena, which often relate to deep ideas in mathematics. There is currently a considerable focus on the interrelations between quantum mechanics and information theory, and on consequences for computation, thermodynamics and other areas of science. Again, researchers in Bristol have made major contributions to the foundations of this area of research.

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Quantum mechanics

Bristol is a world leader in quantum mathematics. The research covers quantum chaos, quantum information and random matrix theory and will be used, for example, to model the complex quantum relationships in tomorrow's computer chips, microlasers and nanoscale systems.